21 Calculate the coordinates of the point of intersection I of the two lines : 1° (D) : x + 3 = 0 2° (D) : y= x- 4 (D'): y = 2x +1 (D') : 4x + y + 3 = 0

Q: Determine the angle between the two lines: 1₁: 7 = (1,0) + t(0, —2), t ¤ R x+2 y-3 and 1₂: *+² = −³.…

A: Given

Q: Find the distance from the point s(1,-6,2)to the line x = 2 + 3t, y = -4 + t,z = –2t Ans >>d=1.79

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Q: (-2/3 + j2) 4. Express in rectangular form.

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Q: How do the paths r1(t) = (cost,sin t) and r2(t) = (sin t, cost)around the unit circle differ?

A: Given :                   r1(t) = cos t , sin tr2(t) = sin t , cos t

Q: What is the length of the transverse axis?

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Q: Find an equation, in slope-intercept form, of the line tangent to the curve with parametric…

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Q: 3) Find the z-coordinate(s) of the point (s) on the curve y = ³ + 6x² - 2x + 15 where the tangent…

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Q: jw F(w). [a - acos (wr)] - A 1 Tjw jwF(W) = -2A (1-cos (WT)). Tjw jwF(W) = -2A (asin ² (WT)) Tjw How…

A: since we have a trigonometric identity:                                   cos(2θ) =1-2 sin2(θ)⇒ 2…

Q: x-2 What is the equation of the tangent line of y at the point x = 3 ? 2x-5

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Q: x = t – 1 * (D) : y = 2t + 3 x = - t'+ 1 (D') : y = t' - 2

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: : Find the angle between the lines whose direction cosines satisfy the equations 1+m +n=0,1 + m² -n…

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Q: br II) passing through P=(2,-1) and is perpendiculed to the line √x=2-t y=3 In normal form.

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Q: A hamster wheel has a point on the wheel with height modelled by the equation, where h is in cm and…

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Q: Show the curve y(u) = o(u, 1) represents a meridian (line of longitude) on S², while the curve y(v)…

A: Given Information:The curve  and the curve  on .To show:The curve  represents a meridian (line of…

Q: The cartesian equation of the curve x= f ,y = 1-t is : (a)y = 1– x², x 20 (b)y =1-x ,x 2 0 (c) x = 1…

A: The given curve is in paramatric form as following- x=√t y=1-t Where t is a parameter. To find the…

Q: Find the general soladtion of y+5y'=5

A: Given equation is y"+5y=5                          (1) Auxiliary equation to the homogeneous…

Q: Q1) Find equation of line normal to plane 3x + 2y - z = 5 and pass through Origin point.

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Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: